Actually the Serenity prayer as it is known today is part of a prayer that was Written by Saint Francis of Assisi, circa 1550 A.D. The prayer in its entirety is much longer and is beautifully written. In it the Saint expresses His desire to understand rather than to be understood, and many more Godly sentiments.
No, not per se. The serenity prayer was written circa 1934. There is some speculation as to the true author but it is most commonly agreed that Reinhold Niebhur wrote it with the intention of using it in a sermon. The abbreviated prayer is a staple in most 12-step programs. In Christ-centered 12-step programs the entire prayer is recited.
No- this prayer was written by a man and is not in the Bible.